Denote by script A sign(n) the family of isometry classes of compact n-dimensional Alexandrov spaces with curvature ≥ -1, and λk(M) the kth eigenvalue of the Laplacian on M ∈ script A sign(n). We prove the continuity of λk : script A sign(n) → R with respect to the Gromov-Hausdorff topology for each k, n ∈ N, and moreover that the spectral topology introduced by Kasue-Kumura ,  coincides with the Gromov-Hausdorff topology on script A sign(n).
- Alexandrov space
- The Gromov-Hausdorff distance
- The spectral distance
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